On the Inviscid Limit of the 3D Navier-Stokes Equations with Generalized Navier-slip Boundary Conditions

In this paper, we investigate the vanishing viscosity limit problem for the 3-dimensional (3D) incompressible Navier-Stokes equations in a general bounded smooth domain of $R^3$ with the generalized Navier-slip boundary conditions (\ref{VSg}). Some uniform estimates on rates of convergence in $C([0,T],L^2(Ω))$ and $C([0,T],H^1(Ω))$ of the solutions to the corresponding solutions of the idea Euler equations with the standard slip boundary condition are obtained.

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